There has been widespread speculation that Mehsud was killed, along with his wife and bodyguards, after a US drone aircraft fired missiles at his father-in-law's house in the village of Makeen earlier in the week.
Haikmullah Mehsud, who would be a leading contender for the leadership, said that the claims were "black propaganda" aimed at luring the Pakistani Taliban leader into the open so that he could be targeted.
His claims were echoed by Maulana Merajuddin, who heads a delegation representing Mehsud's tribe in Islamabad.
"I believe that what we have heard by media sources during the past few days on the killing of Mehsud is incorrect," he told Al Jazeera.
"My sources from local citizens in Waziristan confirm that Mehsud is alive and doing well."
There has been no physical evidence of Mehsud's death and previous claims of his death have proved to be false, but Pakistani officials are confident that a number of signs point to the fact that he has been killed.
On Saturday, one of Mehsud's bodyguards was buried in the town of Mardan, sources have told Al Jazeera, and there have been reports of a meeting of senior Pakistani Taliban fighters to decide on a successor to Mehsud.
Shah Mehmoud Qureshi, Pakistan's foreign minister, said on Friday that he was "pretty certain" that the missile attack had been succesful.
"Various government agencies have reported so, his own followers have said so, there are people who have been to the funeral and are witness to the burial," he told UK-based BBC radio.
A number of intelligence officials have said that Mehsud's body was buried in Nargosey, a tiny settlement about 1km from the site of the reported attack.
The Associated Press news agency quoted Pakistani intelligence officials as saying that the US missile attack came after Pakistani officials passed on information about Mehsud's whereabouts to the Central Intelligence Agency (CIA).
Pakistan's government formally condemns Washington's use of unmanned drones over its territory as violating Islamabad's sovereignty and acting as a recruiting tool for Taliban in the region.
The US refuses to confirm suspected attacks by its drones, but the US military in Afghanistan and the CIA are the only agencies in the region with the technology.
"If Mehsud turns up alive on television screens it would mean that the joint operation was another joint disaster," Al Jazeera's Kamal Hyder, reporting from Islamabad, said.
"The American drone policy in the tribal areas is almost turning the entire population against the United States, anti-American feeling is very high."
"With [Mehsud] gone, I think there is going to be an internal struggle and disarray in their ranks"
Shah Mehmoud Qureshi,
Pakistani foreign minister
Qureshi said that Mehsud's death could lead to divisions in the Taliban.
"With him gone, I think there is going to be an internal struggle and disarray in their ranks, I think it will set in demobilisation. It is a great success for the forces that are fighting extremism and terrorism in Pakistan," he said.
But Bryan Whitman, a Pentagon spokesman, warned that such groups can "regenerate another leader".
"I don't want to make more than one should of a single individual," he said.
The US and Pakistan have said that Mehsud is linked to al-Qaeda and has been involved in dozens of suicide attacks, beheadings and assassinations, including the killing of Benazir Bhutto, the former Pakistani prime minister.
His estimated 10,000-20,000 fighters have been blamed for a wave of suicide attacks inside Pakistan and on Western forces across the border in Afghanistan.